Problem: N different natural numbers are given. If you select four different ones and set them as $ A $, $ B $, $ C $, $ D $, the following formula

$ \ Frac {A + B} {C --D} $



I want to find the maximum value of.




Given N different natural numbers, choose 4 different from them and create a program to find the maximum value of the above formula.



Input

The input is given in the following format.


N
a1 a2 ... aN


The number N (4 ≤ N ≤ 1000) of natural numbers is given in the first line. The value ai (1 ≤ ai ≤ 108) of each natural number is given in the second line. However, the same natural number does not appear more than once (ai ≠ aj for i ≠ j).

Output

Outputs the maximum value of the above formula as a real number for a given N natural numbers. However, the error must not exceed plus or minus 10-5.

Examples

Input

10
1 2 3 4 5 6 7 8 9 10


Output

19.00000


Input

5
22 100 42 3 86


Output

9.78947


Input

6
15 21 36 10 34 5


Output

18.00000


Input

4
100000 99999 8 1


Output

28571.285714

Solution (in JAVA):

Solution:
import java.util.*;

class Main{
    void solve(){
	int n;
	int[] S;
	Scanner sc = new Scanner(System.in);
	n = sc.nextInt();
	S = new int[n];
	for ( int i = 0; i < n; i++ ) S[i] = sc.nextInt();

	double res = 0.0;
	Arrays.sort(S);

	for ( int d = 0; d < n-1; d++ ){
	    int c = d+1;
	    int a = n-1;
	    int b = n-2;
	    if ( d == n-3 ){
		b = d-1;
	    } else if ( d == n-2 ){
		a = d-2;
		b = d-1;
	    }
	    res = Math.max(res, 1.0*(S[a]+S[b])/(S[c]-S[d]));
	}

	System.out.println(String.format("%.8f", res));
    }

    public static void main(String[] args){
	new Main().solve();
    }
	
}